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Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation

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21–30 of 104 posts

Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation

#21

There's a graveyard of 100s of papers with "approximate near linear time attention." They always hope the speed increase makes up for the lower quality, but it never does. The quadratic time seems inherent to the problem. Indeed, there are lower bounds showing that sub n^2 algorithms can't work: https://arxiv.org/pdf/2302.13214

Dumb question: is the quadratic time complexity for training, inference, or both?

Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation

#22

There's a graveyard of 100s of papers with "approximate near linear time attention." They always hope the speed increase makes up for the lower quality, but it never does. The quadratic time seems inherent to the problem. Indeed, there are lower bounds showing that sub n^2 algorithms can't work: https://arxiv.org/pdf/2302.13214

Dumb question: is the quadratic time complexity for training, inference, or both?

Attention is calculated during the forward pass of the model, which happens in both inference (forward only) and training (forward & backward).

Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation

#23
The best and proven linear attention is the Gated DeltaNet or variations of it, used by Kimi and Qwen. Anyone who thinks linear attention can't work is forgetting that models are a fixed size so attention should always be compressable to be linear. Another way to think of the feasibility of linear attention is that the standard attention mechanism can be made linear simply by removing the softmax so the kv cache stores the kv product as a constant size matrix instead. Softmax just normalizes attention, but it's not theoretically required.

Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation

#24
post #12

There's a graveyard of 100s of papers with "approximate near linear time attention." They always hope the speed increase makes up for the lower quality, but it never does. The quadratic time seems inherent to the problem. Indeed, there are lower bounds showing that sub n^2 algorithms can't work: https://arxiv.org/pdf/2302.13214

I think DeepSeek V3.2 is sub n^2, but it clearly performs quite well, refuting the alleged lower bounds in the paper.

[deleted]

Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation

#25
post #12

There's a graveyard of 100s of papers with "approximate near linear time attention." They always hope the speed increase makes up for the lower quality, but it never does. The quadratic time seems inherent to the problem. Indeed, there are lower bounds showing that sub n^2 algorithms can't work: https://arxiv.org/pdf/2302.13214

I think DeepSeek V3.2 is sub n^2, but it clearly performs quite well, refuting the alleged lower bounds in the paper.

It really isn't sub N^2. The main attention is only O(Nk), but only thanks to a lightning indexer that still has complexity O(N^2). So overall it still has the same complexity; just with a smaller constant factor [1]

> DSA reduces the core attention complexity of the main model from O(L^2) to O(Lk), where k ([1] https://arxiv.org/pdf/2512.02556

Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation

#26

There's a graveyard of 100s of papers with "approximate near linear time attention." They always hope the speed increase makes up for the lower quality, but it never does. The quadratic time seems inherent to the problem. Indeed, there are lower bounds showing that sub n^2 algorithms can't work: https://arxiv.org/pdf/2302.13214

> self-attention is efficiently computable to arbitrary precision with constant cost per token

This paper at least aspires to reproduce 'true' attention, which distinguishes it from many of the others. TBD if its successful in that.

Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation

#27

There's a graveyard of 100s of papers with "approximate near linear time attention." They always hope the speed increase makes up for the lower quality, but it never does. The quadratic time seems inherent to the problem. Indeed, there are lower bounds showing that sub n^2 algorithms can't work: https://arxiv.org/pdf/2302.13214

I think any kind of innovation here will have to take advantage of some structure inherent to the problem, like eliminating attention in favour of geometric structures like Grassman flows [1].

[1] Attention Is Not What You Need, https://arxiv.org/abs/2512.19428

Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation

#28

There's a graveyard of 100s of papers with "approximate near linear time attention." They always hope the speed increase makes up for the lower quality, but it never does. The quadratic time seems inherent to the problem. Indeed, there are lower bounds showing that sub n^2 algorithms can't work: https://arxiv.org/pdf/2302.13214

> self-attention is efficiently computable to arbitrary precision with constant cost per token This paper at least aspires to reproduce 'true' attention, which distinguishes it from many of the others. TBD if its successful in that.

It's like claims of room temperature superconductors or millenium prize solutions. Earth shattering if true. It'd be such a black swan. Terrible for Nvidia.

Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation

#29

Earlier quoted context omitted.

> this is where the taylor expression would fail to represent the values well. "In practice, we find that four Taylor terms (P = 4) suffice for recovering conventional attention with elementwise errors of approximately the same magnitude as Float16 resolution"

I read that too, but I wondered whether elementwise error is the right metric. Surely the actual error metric should be to evaluate model performance for a conventional transformer model and then the same model with the attention mechanism replaced by this 4th order Taylor approximation?

Bounded error weights by definition is a more strict evaluation criterion than “performance” metrics through running the model.

Re: Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation

#30
post #22

Earlier quoted context omitted.

Dumb question: is the quadratic time complexity for training, inference, or both?

Attention is calculated during the forward pass of the model, which happens in both inference (forward only) and training (forward & backward).

Dumb question: Can inference be done in a reverse pass? Outputs predicting inputs?
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